Interferometric millimeter wave and thz wave doppler radar

ABSTRACT

A mixerless high frequency interferometric Doppler radar system and methods has been invented, numerically validated and experimentally tested. A continuous wave source, phase modulator (e.g., a continuously oscillating reference mirror) and intensity detector are utilized. The intensity detector measures the intensity of the combined reflected Doppler signal and the modulated reference beam. Rigorous mathematics formulas have been developed to extract bot amplitude and phase from the measured intensity signal. Software in Matlab has been developed and used to extract such amplitude and phase information from the experimental data. Both amplitude and phase are calculated and the Doppler frequency signature of the object is determined.

STATEMENT OF GOVERNMENT INTEREST

The United States Govemment has rights in the invention described hereinpursuant to Contract No. DE-AC02-06CH11357 between the United StatesDepartment of Energy and UChicago Argonne, LLC, as operator of ArgonneNational Laboratory.

FIELD OF THE INVENTION

The field of the invention generally relates to Doppler radar and morespecifically certain implementations relate to interferometricmillimeter wave and THz wave Doppler radar.

BACKGROUND OF THE INVENTION

Doppler sensors have become widely used and utilize various frequencies.At microwave frequencies, Doppler sensors are usually realized throughthe use of quadrature mixers. Microwave based sensors have inherentlylower sensitivity (greater than micrometer displacements) than theiroptical counterparts. High frequency optical Doppler sensor has highsensitivity and lower interference with common consumer electronics.Further, high frequency optical Doppler sensor is more directional andprovides for more compact structures. However, high-frequency opticalsensors have several drawbacks, such as difficulty with alignment anddiffraction loss due to surface roughness. Therefore, optical Dopplersensors are not desirable for applications involving the detection ofcomplex objects. Furthermore, optical wavelengths cannot penetratethrough many common materials such as fabrics, plastics and insulation.

As both low frequency microwaves and high frequency optics haveadvantages and disadvantages, certain systems have attempted to use theintermediate frequency spectrum between the low-frequency microwaves andthe high-frequency optics. For example, quadrature mixer based mmWDoppler radar has been recently studied for remote monitoring of vitalsigns by the authors' group.

SUMMARY OF THE INVENTION

One embodiment relates to a Doppler system for detecting an object. Thesystem comprises a continuous wave source. Further, a beam splitter isprovided. The system also includes a phase modulator and an intensitydetector.

In another embodiment, a method of detecting an object is provided. Acontinuous wave beam is emitted. The continuous wave beam is split intoan object beam and a reference beam. The object beam is directed to theobject. The reference beam is directed to a phase modulator. The phaseof the reference beam is modulated to generate a modulated referencebeam. An intensity detector receives the modulated reference beam and areflected Doppler signal from the object.

In another embodiment, a method of processing Doppler information isprovided. A Doppler signal is received from an object. A referencesignal is modulated. The combined intensity of the Doppler signal andthe modulated reference beam is measured. The measured combinedintensity is separated into Low-Frequency-Band and High-Frequency-Bandsignals. The amplitude and phase of the reflected signal from the objectare determined. The Doppler frequency signature of the object based uponthe determined amplitude and phase is determined.

Additional features, advantages, and embodiments of the presentdisclosure may be set forth from consideration of the following detaileddescription, drawings, and claims. Moreover, it is to be understood thatboth the foregoing summary of the present disclosure and the followingdetailed description are exemplary and intended to provide furtherexplanation without further limiting the scope of the present disclosureclaimed.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other objects, aspects, features, and advantages ofthe disclosure will become more apparent and better understood byreferring to the following description taken in conjunction with theaccompanying drawings, in which:

FIG. 1 illustrates schematics of an implementation of an interferometricDoppler radar.

FIG. 2 illustrates simulated 94-GHz intensity I(t).

FIG. 3 illustrates LFB (Low Frequency Band) and HFB (High FrequencyBand) signals of I(t) in FIG. 2.

FIG. 4 illustrates amplitude a_(obj)(t) and phase φ_(obj)(t) obtainedfrom LFB and HFB signals in FIG. 3: comparisons between reconstructedvalues and initial values in Eq. (20).

FIG. 5 is a graph of measured 94-GHz intensity I(t) for a ball pendulumof small amplitude.

FIG. 6 is a zoom view of a small segment of I(t) in FIG. 5 to show the200 Hz modulation of one single cycle for approximately t<45 seconds.

FIG. 7 (top) illustrates LFB signal from Eq. (7), and FIG. 7 (bottom)illustrates HFB signal from Eq. (10).

FIG. 8 (top) illustrates amplitude a_(obj)(t), and FIG. 8 (bottom)illustrates phase φ_(obj)(t).

FIG. 9 illustrates Doppler signature: Fourier transform of φ_(obj)(t)given in FIG. 8.

FIG. 10 (top) illustrates measured intensity I(t) for a ball pendulum ofsmall amplitude; and FIG. 10 (bottom) illustrates zoom view of the first0.5 second.

FIG. 11 (top) illustrates a HFB signal from Eq. (10); and FIG. 11(bottom) illustrates a LFB signal from Eq. (7).

FIG. 12 (top) illustrates amplitude a_(obj)(t) and FIG. 12 (bottom)phase φ_(obj)(t).

FIG. 13 illustrates a frequency signature obtained through Fouriertransform of φ_(obj)(t) given in FIG. 12.

FIG. 14 (top) is measured intensity I(t) for a ball pendulum of largeamplitude; and FIG. 14 (bottom) is a zoom view of the first 0.5 second.

FIG. 15 (top) HFB signal from Eq. (10), and FIG. 15 (bottom) is a LFBsignal from Eq. (7).

FIG. 16 (top) illustrates amplitude a_(obj)(t), and FIG. 16 (bottom)illustrates phase φ_(obj)(t).

FIG. 17 Frequency signature obtained through Fourier transform ofφ_(obj)(t) given in FIG. 16.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

In the following detailed description, reference is made to theaccompanying drawings, which form a part hereof. In the drawings,similar symbols typically identify similar components, unless contextdictates otherwise. The illustrative embodiments described in thedetailed description, drawings, and claims are not meant to be limiting.Other embodiments may be utilized, and other changes may be made,without departing from the spirit or scope of the subject matterpresented here. It will be readily understood that the aspects of thepresent disclosure, as generally described herein, and illustrated inthe figures, can be arranged, substituted, combined, and designed in awide variety of different configurations, all of which are explicitlycontemplated and made part of this disclosure.

In one implementation, a universal, mixerless high frequencyinterferometric Doppler radar is provided. The implementation amploysthe optical interferometry technique that requires no quadrature mixer.It also differs from other conventional Mach-Zehnder interferometry inthat it adopts a continuously oscillating reference mirror to modulatethe Doppler signal. By doing this, both amplitude and phase can beextracted from only one intensity measurement In a particularimplementation, millimeter wavelengths and THz wavelengths are utilizedwith optical interferometry technique by using a CW (Continuous Wave)source and an intensity detector. A beam splitter is further utilizedand a phase modulator. The detected intensity is the coherent additionof the reference beam and the reflected signal, which, in oneimplementation, features a fast reference modulation on a slowmodulation induced by the object. As further set forth below, rigorousmathematical formulations are provided to solve for both the amplitudeand the phase simultaneously. Once the phase is known, Fourier transformis then used to study the Doppler frequency signature of a movingobject. Examples are also set forth below a 94 GHz prototype and a 0.15THz prototype utilized in experimental tests using a ball pendulumtarget with full-swing distance much smaller than a wavelength to studythe performance of the proposed interferometric Doppler radar.

FIG. 1 shows the architecture of one implementation of a Doppler radar,which is based on the Michelson interferometry optical technique using aCW (optionally frequency tunable, e.g., backward wave oscillator andquantum cascade laser etc.) source 101 and an intensity detector 140.The source wave 102 is first collimated into a parallel beam, which isthen split into two beams, with one, an object beam 110, propagatingtowards the moving object and the other, reference beam 111, serving asthe reference beam modulated by a phase modulator 160, such as ancontinuously oscillating mirror or other electronically controlled phasemodulators. The reflected Doppler signal 120 by the moving object 150 isthen combined with the modulated reference beam 130 and fed into anintensity detector 140. The oscillating mirror 160 modulates theLow-Frequency-Band (LFB) Doppler signature to the High-Frequency-Band(HFB) Doppler centered at the reference arm frequency of the phasemodulator.

For broadband Doppler signature, the reference arm frequency needs tooscillate at a frequency that is higher than twice the Doppler frequencyof the object to avoid overlapping of the LFB and HFB signals; while fornarrowband Doppler signature (e.g., moving cars and aircrafts etc.), thereference arm frequency only needs to >2× the bandwidth of the Dopplersignature interferometric Doppler radar relies upon the effect of aphase modulator, operating at 2F_(max) to modulate the Doppler spectrumto its HFB and its LFB spectrum. The unknown amplitude and phase arederived from the measured HFB and LFB.

One implementation of the Doppler radar provides a system without theneed for mixer based homodyne or heterodyne radar. For implementationsutilizing mmW, a mmW Gunn Oscillator may be used. Implementations canalso be provided at the THz gap. For example, as THz source either aBackward Wave Oscillator (BWO) or a THz Quantum Cascade Laser (QCL)could replace the mmW Gunn Oscillator and as intensity detector either apyroelectric detector or a Hot Electron Bolometer (HEB) can be used. ThemmW/THz interferometric Doppler radar has many applications, includingvibration/displacement measurement (down to few μm), coating/thin filmthickness measurement, dielectric constant characterization,phase-sensitive chemicals spectroscopy and phase-contrastNon-Destructive Evaluation (NDE) of dielectric materials.

In one implementation, the phase modulator 160 is a mechanicallyvibrating mirror, which is different from the stationary steepingMach-Zehnder type interferometry such as FTIR. In anotherimplementation, the phase modulator is an electronically controllabledielectric material. Examples of such phase modulators 160 include, butare not limited to, Pockel cells, liquid crystal modulators, and thelike. Further, it is possible to utilize thermally induced refractiveindex changes or length changes, such as of an optical fiber or inducedlength changes by stretching.

Mathematically, the intensity detector detects the combined reflectedsignal from the object E_(obj)(t) and the reference beam E_(ref)(t),plus the background E_(b),

$\begin{matrix}{{E(t)} = {{{E_{obj}(t)} + {E_{ref}(t)} + E_{b}} = {{{a_{obj}(t)}^{{j\varphi}_{obj}{(t)}}} + {a_{ref}^{{j\varphi}_{ref}{(t)}}} + {a_{b}^{{j\varphi}_{b}}}}}} & (1)\end{matrix}$

where a_(obj)(t), a_(ref), and a_(b) are the amplitudes of the reflectedsignal, the reference beam and the background respectively; φ_(obj)(t),φ_(ref)(t) and φ_(b) are their corresponding phases. The detectedintensity is thus given by

I(t)=|E(t)|² =a _(obj) ²(t)+a _(ref) ² +a _(b) ²+2a _(obj)(t)a _(b)cos|φ_(obj)(t)−φ_(b)|+2a _(ref) a _(b) cos|φ_(ref)(t)−φ_(b)|+2a _(ref) a_(obj)(t)cos|φ_(ref)(t)−φ_(obj)(t)|  (2)

The intensity signal given in Eq. (2) can be separated into LFB(Low-Frequency-Band) and HFB (High-Frequency-Band) signals. Toillustrate this, let us decompose the reference phase φ_(ref)(t) intoFourier series,

$\begin{matrix}{{\varphi_{ref}(t)} = {\varphi_{0} + {\sum\limits_{m = 1}^{\infty}\; {c_{m}{\cos \left( {m\; \omega_{ref}t} \right)}}}}} & (3)\end{matrix}$

Consider the following term given in Eq. (2),

$\begin{matrix}\begin{matrix}{{2a_{ref}a_{b}{\cos \left\lbrack {{\varphi_{ref}(t)} - \varphi_{b}} \right\rbrack}} = {a_{ref}a_{b}\left\{ {^{j{({{\varphi_{ref}{(t)}} - \varphi_{b}})}} + ^{- {j{({{\varphi_{ref}{(t)}} - \varphi_{b}})}}}} \right\}}} \\{= {a_{ref}a_{b}\left\{ {{^{{- j}{\overset{\sim}{\varphi}}_{b}}^{j{\sum\limits_{m = 1}^{\infty}\; {c_{m}{\cos {({m\; \omega_{ref}t})}}}}}} +} \right.}} \\\left. {^{j{\overset{\sim}{\varphi}}_{b}}^{{- j}{\sum\limits_{m = 1}^{\infty}\; {c_{m}{\cos {({m\; \omega_{ref}t})}}}}}} \right\} \\{= {a_{ref}a_{b}\begin{Bmatrix}{{^{{- j}{\overset{\sim}{\varphi}}_{b}}{\prod\limits_{m = 1}^{\infty}\; \begin{bmatrix}{{J_{0}\left( c_{m} \right)} + 2} \\{\sum\limits_{n = 1}^{\infty}\; \left\lbrack {j^{n}{J_{n}\left( c_{m} \right)}{\cos \left( {n\; m\; \omega_{ref}t} \right)}} \right\rbrack}\end{bmatrix}}} +} \\{^{j{\overset{\sim}{\varphi}}_{k}}{\prod\limits_{m = 1}^{\infty}\; \begin{bmatrix}{{J_{0}\left( c_{m} \right)} + 2} \\{\sum\limits_{n = 1}^{\infty}\; \left\lbrack {\left( {- j} \right)^{n}{J_{n}\left( c_{m} \right)}{\cos \left( {n\; m\; \omega_{ref}t} \right)}} \right\rbrack}\end{bmatrix}}}\end{Bmatrix}}}\end{matrix} & (4)\end{matrix}$

where Jacobi-Anger expansion has been used. J₀ is Bessel function of thefirst kind with order 0 and {tilde over (φ)}_(b)=φ_(b)−φ₀.

The LFB signal from Eq. (4) is given by

$\begin{matrix}{{2a_{ref}a_{b}{\cos \left\lbrack {{\varphi_{ref}(t)} - \varphi_{b}} \right\rbrack}_{LFB}} \approx {2a_{ref}a_{b}{\cos \left( {\overset{\sim}{\varphi}}_{b} \right)}{\prod\limits_{m = 1}^{\infty}\; {J_{0}\left( c_{m} \right)}}}} & (5)\end{matrix}$

Similarly, the following term in Eq. (2) has a LFB signal of

$\begin{matrix}{{2a_{ref}{a_{obj}(t)}{\cos \left\lbrack {{\varphi_{ref}(t)} - {{\overset{\sim}{\varphi}}_{obj}(t)}} \right\rbrack}_{LFB}} \approx {2a_{ref}{a_{obj}(t)}{\cos \left( {{\overset{\sim}{\varphi}}_{obj}(t)} \right)}{\prod\limits_{m = 1}^{\infty}\; {J_{0}\left( c_{m} \right)}}}} & (6)\end{matrix}$

where {tilde over (φ)}_(obj)(t)=φ_(obj)(t)−φ₀.Hence the intensity given in Eq. (2) has the LFB signal of

$\begin{matrix}{{I(t)}_{LFB}{\approx {{a_{obj}^{2}(t)} + a_{ref}^{2} + a_{b}^{2} + {2\; {a_{obj}(t)}a_{b}{\cos \left\lbrack {{{\overset{\sim}{\varphi}}_{obj}(t)} - {\overset{\sim}{\varphi}}_{b}} \right\rbrack}} + {2\; a_{ref}{\prod\limits_{m = 1}^{\infty}\; {{J_{0}\left( c_{m} \right)}\left\{ {{a_{b}{\cos \left( {\overset{\sim}{\varphi}}_{b} \right)}} + {{a_{obj}(t)}{\cos \left( {{\overset{\sim}{\varphi}}_{obj}(t)} \right)}}} \right\}}}}}}} & (7)\end{matrix}$

The amplitude of the HFB signal of the following term in Eq. (2) isgiven by

$\begin{matrix}{{2\; a_{ref}a_{b}{\cos \left\lbrack {{\varphi_{ref}(t)} - \varphi_{b}} \right\rbrack}_{HFB}} \approx {2\; a_{ref}a_{b}{\sin \left( {\overset{\sim}{\varphi}}_{b} \right)}{J_{1}\left( c_{1} \right)}{\prod\limits_{m = 2}^{\infty}\; {J_{0}\left( c_{m} \right)}}}} & (8)\end{matrix}$

Similarly, the following term in Eq. (2) has HFB signal amplitude of

$\begin{matrix}{{2\; a_{ref}{a_{obj}(t)}{\cos \left\lbrack {{\varphi_{ref}(t)} - {{\overset{\sim}{\varphi}}_{obj}(t)}} \right\rbrack}_{HFB}} \approx {4\; a_{ref}{a_{obj}(t)}{\sin \left( {{\overset{\sim}{\varphi}}_{obj}(t)} \right)}{J_{1}\left( c_{1} \right)}{\prod\limits_{m = 2}^{\infty}\; {J_{0}\left( c_{m} \right)}}}} & (9)\end{matrix}$

Hence the intensity given in Eq. (2) has the HFB signal of

$\begin{matrix}{{I(t)}_{HFB}{\approx {4\; a_{ref}{J_{1}\left( c_{1} \right)}{\prod\limits_{m = 2}^{\infty}\; {{J_{0}\left( c_{m} \right)}\left\{ {{{a_{obj}(t)}{\sin \left( {{\overset{\sim}{\varphi}}_{obj}(t)} \right)}} + {a_{b}{\sin \left( {\overset{\sim}{\varphi}}_{b} \right)}}} \right\}}}}}} & (10)\end{matrix}$

The LFB and HFB signals when there is no background is obtained from Eq.(7) and Eq. (10)

$\begin{matrix}{{{I(t)}_{LFB}{\approx {{a_{obj}^{2}(t)} + a_{ref}^{2} + {2\; a_{ref}{\prod\limits_{m = 1}^{\infty}\; {{J_{0}\left( c_{m} \right)}{a_{obj}(t)}{\cos \left( {{\overset{\sim}{\varphi}}_{obj}(t)} \right)}}}}}}}{{I(t)}_{HFB}{\approx {4\; a_{ref}{J_{1}\left( c_{1} \right)}{\prod\limits_{m = 1}^{\infty}\; {{J_{0}\left( c_{m} \right)}{a_{obj}(t)}{\sin \left( {{\overset{\sim}{\varphi}}_{obj}(t)} \right)}}}}}}} & (11)\end{matrix}$

The amplitude and phase of the Doppler signal of the moving object canbe solved from the LFB signal in Eq. (7) and HFB signal in Eq. (10),

x _(c)(t)² +Bx _(c)(t)+C=l(t)|_(LFB)  (12)

where we have the following definitions:

$\begin{matrix}{\mspace{79mu} {{{x_{c}(t)} \equiv {{a_{obj}(t)}{\cos \left( {{\overset{\sim}{\varphi}}_{obj}(t)} \right)}}}\mspace{79mu} {B = {{2\; a_{b}{\cos \left( {\overset{\sim}{\varphi}}_{b} \right)}} + {2\; a_{ref}{\prod\limits_{m = 1}^{\infty}{J_{0}\left( c_{m} \right)}}}}}{C = {{{{x_{s}(t)}^{2} + a_{ref}^{2} + a_{b}^{2} + {2\; a_{b}{\sin \left( {\overset{\sim}{\varphi}}_{b} \right)}{x_{s}(t)}} + {2\; a_{ref}a_{b}{\cos \left( {\overset{\sim}{\varphi}}_{b} \right)}{\prod\limits_{m = 1}^{\infty}{J_{0}\left( c_{m} \right)}}} - {I(t)}}_{LFB}{{x_{s}(t)} \equiv {{a_{obj}(t)}{\sin \left( {{\overset{\sim}{\varphi}}_{obj}(t)} \right)}}}} = {\left\lbrack {{I(t)}_{HFB}{{/4}\; a_{ref}{J_{1}\left( c_{1} \right)}{\prod\limits_{m = 2}^{\infty}{J_{0}\left( c_{m} \right)}}}} \right\rbrack - {a_{b}{\sin \left( {\overset{\sim}{\varphi}}_{b} \right)}}}}}}} & (13)\end{matrix}$

Where c_(m) is the reference mirror oscillating amplitudes at mthharmonics frequency; a_(obj) and a_(ref) are the object and referencemirror amplitudes respectively; I(t) is the measured intensity signal;and J0, J1 are the Bessel functions of zero/first order respectively.The variable x_(c)(t) can be solved from Eq. (1),

$\begin{matrix}{{x_{c}(t)} = \frac{{- B} \pm \sqrt{B^{2} - {4\; C}}}{2}} & (14)\end{matrix}$

Combining Eq. (1) and Eq. (2), we obtain the amplitude and phase

a _(obj)(t)=√{square root over (x _(c)(t)² +x _(x)(t)²)}{square rootover (x _(c)(t)² +x _(x)(t)²)};{tilde over (φ)}_(obj)(t)=arctan [x_(s)(t)/x _(c)(t)]  (15)

Alternatively, if one wants to calculate only the phase (t), a simplerformula can be used:

$\begin{matrix}{{{\overset{\sim}{\varphi}}_{obj}(t)} = {\arctan \left\lbrack {- \frac{{{J_{2}\left( c_{1} \right)}{I(t)}}_{HFB}}{{{J_{1}\left( c_{1} \right)}{I(t)}}_{{HFB}\; 2}}} \right\rbrack}} & (16)\end{matrix}$

With J₂ being the Bessel function of order 2, and I(t)|_(HFB) andI(t)|_(HFB2) are first HFB and second HFB signals centered at firstharmonics reference frequency and second harmonics reference frequencyrespectively.

When background is absent, the coefficients in Eq. (13) are given by,

$\begin{matrix}{{B = {2\; a_{ref}{\prod\limits_{m = 1}^{\infty}\; {J_{0}\left( c_{m} \right)}}}}\begin{matrix}{C = {{{x_{s}(t)}^{2} + a_{ref}^{2} - {I(t)}}_{LFB}{x_{s}(t)}}} \\{\equiv {{a_{obj}(t)}{\sin \left( {{\overset{\sim}{\varphi}}_{obj}(t)} \right)}}} \\{= {{I(t)}_{HFB}{{/4}\; a_{ref}{J_{1}\left( c_{1} \right)}{\prod\limits_{m = 2}^{\infty}\; {J_{0}\left( c_{m} \right)}}}}}\end{matrix}} & (17)\end{matrix}$

After obtaining the reflected sub-THz signal complex field (amplitudeand phase), the Doppler frequency signature of the moving object can beanalyzed. The Doppler frequency f_(Doppler)(t) from the carrierfrequency f is given by

$\begin{matrix}{{f_{Doppler}(t)} = {2\frac{v(t)}{c}f}} & (18)\end{matrix}$

where v(t) is the object velocity and c is the speed of light. TheDoppler frequency is closely related to the phase φ_(obj)(t) of thereflected signal for the object displacement x(t),

$\begin{matrix}{{f_{Doppler}(t)} = {\frac{{\varphi_{obj}(t)}}{t} = {\frac{4\; \pi}{\lambda}\frac{{x(t)}}{t}}}} & (19)\end{matrix}$

where λ is the carrier wavelength. Eq. (19) has taken into account theround trip of the carrier wave.

Numerical Simulation

Before the experiment, a numerical simulation was performed to confirmthe mathematical derivation given above. The following parameters areused for numerical simulation:

E(r)=[1+0.1 cos(40πt)/]e ^(j0.2056 cos(40π))+e^(j0.1262 cos(400π)) +e^(j2.6801) +n(t)  (20)

where n(t) is the added noise so that the SNR is 10 dB during thesimulation. The intensity I(t) plot is shown in FIG. 2. The calculatedLFB and HFB signals are shown in FIG. 3. The reconstructed amplitudea_(obj)(t) and phase φ_(obj)(t) are shown as circles in FIG. 4, withgreat agreements with the initial values (lines) in Eq. (20).

Example 1

To test the performance of the proposed interferometric Doppler radar, a94 GHz prototype was built using a Gunn oscillator as source 101 and aSchottky Barrier (SB) diode as intensity detector 140. The phasemodulator 160 was a reference mirror is oscillating at a frequency of200 Hz with displacement amplitude of A_(mirror)≈0.03 mm, which is muchsmaller than the wavelength of λ≈3.2 mm. This corresponds to thefollowing parameters in Eq. (4): c_(j)=4πA_(mirror)/λ≈0.1181,J₁(c_(m))≈0.0588, J₀(c_(m))≈0, m=2, 3, 4 . . . ; c_(m)≈0, J₀(c_(m))≈1,m==1, 2, 3 . . . . During the experiment, a swinging ball pendulum withlength L≈15 cm was used as the moving object, giving a swing frequencyof

${f_{pendulum} \approx {\frac{1}{2\; \pi}\sqrt{\frac{g}{L}}}} = {{\frac{1}{2\; \pi}\sqrt{\frac{9.8}{L}}} \approx {1.286\mspace{14mu} {{Hz}.}}}$

The full swing distance of the pendulum was set to D_(pendulum)=0.25 mm,much smaller than the carrier wavelength of λ≈3.2 mm.

A sample segment of the measured intensity I(t) is shown in FIG. 5. Thesignal before approximately 45 s was collected with the reference mirroroscillating at 200 Hz. The reference mirror is kept stationary afterapproximately 45 s. FIG. 6 shows the close up of a small segment of themeasured intensity I(t) shown in FIG. 5. The 200 Hz modulation isevident before approximately 45 s with no modulation when the referencemirror ceased to oscillate after approximately 45 s.

The LFB signal given in Eq. (7) and HFB signal given in Eq. (10) areshown in FIG. 7 (top) and FIG. 7 (bottom) respectively. With LFB and HFBsignals now available, the amplitude and phase can be obtained bysolving Eq. (12) to Eq. (15) with the results shown in FIGS. 8 a-b. Thedisplacement amplitude of the object a_(obj)(t) is shown in FIG. 8(top), which has a mean value of ā_(obj)(t)=0.0028. FIG. 8 (bottom)shows the displacement phase of the object φ_(obj)(t). The full-swingphase, i.e., difference between phase maximum φ_(obj)(t)|_(max) andphase minimum φ_(obj)(t)|_(min), is ≈58R, which corresponds to afull-swing distance of D_(measured)≈0.2571 mm, agreeing well with theexperimentally set swing value of D_(pendulum)=0.25 mm. The Dopplerfrequency signature can be obtained by taking the Fourier transform ofφ_(obj)(t) given in FIG. 8 (bottom). The result of the transformation isshown in FIG. 9. The measured pendulum frequency is f_(measured)≈1.275Hz, agreeing well with the theoretically calculated value off_(pendulum)≈11.286 Hz. Finally, the sensitivity of the 94-GHz prototypewas determined to be ˜5 degrees, which corresponding to ˜45 μmdisplacement accuracy.

This example utilized a universal, mixerless interferometric Dopplerradar architecture employing a CW source and an intensity detector. Amotorized oscillating reference mirror was used to modulate theintensity at a frequency higher than twice the object's Dopplerfrequency. The 94-GHz prototype was built and tested using a ballpendulum target with a full-swing distance much smaller than the carrierwavelength. The mathematical formulation set forth above was derived toextract both the amplitude and the phase of the Doppler signal bydecomposing the measured intensity into LFB and HFB signals. Themeasurement results were shown to agree well with the experimentallyadjusted parameters such as pendulum frequency and full-swing distance.

Experiment 2

To further test the performance of the proposed interferometric Dopplerradar, a 0.15-THz prototype was built using Gunn oscillator as a source101 and Schottky Barrier (SB) diode as an intensity detector 140. Thephase modulator 160 was a reference mirror oscillating at a frequency of190 Hz with amplitude of A_(mirror)≈0.0388 mm, much smaller than thewavelength of λ=2 mm. This corresponds to the following parameters inEq. (4):

c₁=4πA_(mirror)/λ≈0.1218, J₁(c₁)≈0.0608, J₁(c_(m))≈0, m=2, 3, 4 . . . ;c_(m)≈0, J₀(c_(m))≈1, m=1, 2, 3 . . . . During the experiment, aswinging ball pendulum with length L≈18 cm is used as the Dopplerobject, giving a swing frequency of

$f_{pendulum} \approx {\frac{1}{2\; \pi}\sqrt{\frac{g}{L}}} \approx {1.17\mspace{14mu} {{Hz}.}}$

The full swing distance of the swinging pendulum was set to a value muchsmaller than the carrier wavelength of λ=2 mm.

Experimental results are provided for two typical cases: 1) phase changesmaller than 2π; and 2) phase change larger than 2π. In the case ofphase change smaller than 2π, the full swing distance of the swingingpendulum was set to D_(pendulum)=−0.95 mm. The measured intensity I(t)is shown in top plot of FIG. 10 (top) and the zoom view of the first 0.5second is shown in the bottom plot of FIG. 10 (bottom). The LFB signalgiven in Eq. (7) and HFB signal given in Eq. (10) are shown in top andbottom plots of FIG. 11 (top) and FIG. 11 (bottom) respectively.

With LFB and HFB signals obtained in FIGS. 11 a-b, both amplitude andphase can be obtained by solving Eq. (12) to Eq. (14); FIG. 12 shows theobtained amplitude a_(obj)(t) and the phase φ_(obj)(t) of the object.The full-swing phase, i.e., difference between phase maximumφ_(obj)(t)|_(max) and phase minimum φ_(obj)(t)|_(min), is obtained as≈344°, which corresponds to a full-swing distance of D_(measured)≈0.96mm, agreeing well with the experimentally set value of D_(pendulum)=0.95mm. Doppler frequency signature can be obtained through Fouriertransform of φ_(obj)(t) given in FIG. 13, which is shown in FIG. 12. Theobtained pendulum frequency is f_(measured)≈1.21 Hz, agreeing well withthe aforementioned theoretical calculated value of f_(pendulum)≈1.17 Hz.

In the case of phase change larger than 2π, the full swing distance ofthe swinging pendulum was set to D_(pendulum)=1.85 mm. The measuredintensity I(t) is shown in top plot of FIG. 14 (top) and the zoom viewof the first 0.5 seconds is shown in the bottom plot of FIG. 14(bottom). The LFB signal given in Eq. (7) and HFB signal given in Eq.(10) are shown in top and bottom plots of FIG. 15 a (top) and FIG. 15(bottom) respectively.

With LFB and HFB signals obtained in FIG. 15, both amplitude andunwrapped phase can be obtained by solving Eq. (12) to Eq. (14); FIG. 16shows the obtained amplitude a_(obj)(t) and the phase φ_(obj)(t) of theobject. The full-swing phase, i.e., difference between phase maximumφ_(obj)(t)|_(max) and phase minimum φ_(obj)|_(min), is obtained as≈666°, which corresponds to a full-swing distance of D_(measured)≈1.8503mm, agreeing well with the experimentally set value of D_(pendulum)≈1.5mm. Doppler frequency signature can be obtained through Fouriertransform of φ_(obj)(t) given in FIG. 17, which is shown in FIG. 16. Theobtained pendulum frequency is f_(measured)≈1.16 Hz, compared with thetheoretical calculated value of f_(pendulum)≈1.17 Hz.

This example reflects a mixer less interferometric 0.15-THz Dopplerradar. The sub-THz Doppler radar architecture consisted of just a CWsource and a Shottky diode intensity detector. A motorized oscillatingreference mirror was used to modulate the intensity at a frequencyhigher than twice the object's Doppler frequency. The mathematicalformulation above were used to extract both the amplitude and theunambiguous unwrapped phase of the Doppler signal by decomposing themeasured intensity into LFB and HFB signals.

The foregoing description of illustrative embodiments has been presentedfor purposes of Illustration and of description. It is not intended tobe exhaustive or limiting with respect to the precise form disclosed,and modifications and variations are possible in light of the aboveteachings or may be acquired from practice of the disclosed embodiments.It is intended that the scope of the invention be defined by the claimsappended hereto and their equivalents.

What is claimed is:
 1. A Doppler system for detecting an object,comprising: a continuous wave source; a beam splitter; a phasemodulator; and an intensity detector.
 2. The system of claim 1, whereinthe beam splitter positioned to receive a continuous wave beam from thecontinuous wave source and split the beam into an object beam directedto the object and a reference beam directed to the phase modulator; 3.The system of claim 1, wherein the beam splitter further positioned toreceive a modulated reference beam from the phase modulator and areflected Doppler signal from the object
 4. The system of claim 1,wherein the continuous wave source is configured to provide
 5. Thesystem of claim 1, wherein the phase modulator is an oscillating mirror.6. The system of claim 5, wherein the oscillating mirror oscillates at afrequency at least twice the frequency of a received Doppler signalreflected from the object.
 7. The system of claim 1, wherein thecontinuous wave source is configured to emit millimeter waves orterahertz waves.
 8. The system of claim 1, wherein the continuous wavesource is configured to emit frequencies between 0.085 THz and 0.3 THz.9. A method of detecting an object comprising; emitting a continuouswave beam; splitting the continuous wave beam into an object beam and areference beam; directing the object beam to the object; directing thereference beam to a phase modulator, modulating the phase of thereference beam to generate a modulated reference beam; and receiving atan intensity detector the modulated reference beam and a reflectedDoppler signal from the object.
 10. The method of claim 9, wherein thefirst continuous wave beam is collimated into a parallel continuous wavebeam prior to being split.
 11. The method of claim 9, where modulatingthe phase comprises modulating the reference beam Low-Frequency-Band(LFB) Doppler signature to the High-Frequency-Band (HFB) Dopplercentered at a reference frequency of the phase modulator.
 12. The methodof claim 11, wherein the reference frequency is at least twice theDoppler frequency of the object.
 13. The method of claim 9, comprisingdetermining the amplitude and phase of the reflected signal from theobject;
 14. The method of claim 13, comprising determining the Dopplerfrequency signature of the object based upon the determined amplitudeand phase.
 15. A method of processing Doppler information comprising:receiving a Doppler signal from an object; modulating a referencesignal: measuring the combined intensity of the Doppler signal and themodulated reference beam separating the measured combined intensity intoLow-Frequency-Band and High-Frequency-Band signals; determining theamplitude and phase of the reflected signal from the object; determiningthe Doppler frequency signature of the object based upon the determinedamplitude and phase.
 16. The method of claim 15, wherein the measurementof the combined intensity comprises combining the reflected signal fromthe object E_(obj)(t) and the reference beam E_(ref)(t), $\begin{matrix}{{E(t)} = {{E_{obj}(t)} + {E_{ref}(t)} + E_{b}}} \\{= {{{a_{obj}(t)}^{j\; {\varphi_{obj}{(t)}}}} + {a_{ref}^{j\; {\varphi_{ref}{(t)}}}} + {a_{b}^{j\; \varphi_{b}}}}}\end{matrix}$ where a_(obj)(t) and a_(ref) are the amplitudes of thereflected signal and the reference beam respectively.
 17. The method ofclaim 16, wherein determining the Doppler frequency signature comprises:${f_{Doppler}(t)} = {\frac{{\varphi_{obj}(t)}}{t} = {\frac{4\; \pi}{\lambda}\frac{{x(t)}}{t}}}$where f_(Doppler)(r) is Doppler frequency from the carrier frequency f,v(t) is the object velocity, cis the speed of light, φ_(obj)(t) phase ofthe reflected signal for the object displacement x(t), and λ is thecarrier wavelength.